For 29 years, Alcatraz was the most secure federal prison in the United States, surrounded by the waters of the Pacific Ocean.

Yet brothers John and Clarence Anglin and Frank Morris pulled off a daring prison break in which they disappeared into the night and were never seen nor heard from again - until now.

The three prisoners escaped on the night of June 11, 1962. They squeezed through the vents in their cells - widened with a homemade drill - and escaped on a raft made from more than 50 raincoats.

In the morning guards found their cells empty, with dummy heads made from plaster, papier mache and human hair resting on their pillows.

CBS San Francisco has obtained a letter allegedly written by one of the escapees, forcing the FBI to reopen the famous cold case. It was sent anonymously to San Francisco police in 2013.

"My name is John Anglin," reads the letter. "I escape from Alcatraz in June 1962 with my brother Clarence and Frank Morris. I'm 83 years old and in bad shape. I have cancer. Yes we all made it that night but barely!"

The letter claims that the other two men died in the last 10 years. The writer - whether it really is Anglin or not - makes an offer directly to the FBI.

"If you announce on TV that I will be promised to first go to jail for no more than a year and get medical attention, I will write back to let you know exactly where I am. This is no joke."

The results of the FBI's testing of the letter's authenticity - including handwriting, fingerprints and DNA - were inconclusive.

Authorities remain adamant that all three men drowned that night.

In a statement to CBS San Francisco, the US Marshals Service wrote: "There is absolutely no reason to believe that any of them would have changed their lifestyle and became completely law abiding citizens after this escape."

If the men are alive today, Morris would be 90 while the Anglin brothers would be 86 and 87.